In a conventional flat-surface scanning optical system, a constant-speed scanning system is used as shown in FIG. 1.
In this optical system, a laser beam is emitted from the light source 1 and passes through the collimating lens 2 to form a stream of parallel light 6. The light is then reflected by a reflecting polygon mirror 3 (reflecting rotating mirror 3) and passed through an image lens 4 to form an image on the screen surface 5. The reflecting polygon mirror 3 rotates counterclockwise as shown with arrowhead A and, therefore, the light beam striking the screen surface 5 moves in the direction of arrowhead B.
As a general rule, the relation among the field angle .theta., focal length f and image height y (distance between the center of screen surface 5 and the beam spot on the surface) is as follows: EQU y=f tan .theta. (1)
In other words, the image height y varies in direct proportion to tan .theta.. When the angular velocity .omega. of the reflecting polygonal mirror 3 is a constant, the variation of tan .theta. becomes larger as the rotational angle .theta. becomes larger. This results in variations of the speed at which the light beam moves across the surface of the screen 5.
To eliminate this disadvantage, it is possible to modify the speed of rotation of the reflecting polygon mirror 3 to compensate for the different speed at different angles and control the beam so that it moves at a constant speed. But this procedure is so complicated that it is not easily implemented.
It has been suggested to use a so-called f.theta.lens (image lens) to attain a constant scanning while using a reflecting polygon mirror which rotates at a constant speed. See U.S. Pat. Nos. 4,269,478 and 4,401,362.
The relations in the f.theta. lens are as follows: EQU y=f .theta. (2)
where y is image height, .theta. is field angle, and f is focal length.
When a lens system satisfies the formula (2), the image height y varies constantly when .theta. varies uniformly.
Generally, distortion (D) is defined as follows: ##EQU1## where y' is the actual image height of the beam on the screen surface 5. With an f.theta. lens system, a negative distortion (D) results. In contrast, the aberration of distortion (D) is accordingly modified as D' for the f.theta. lens system. ##EQU2## Naturally, it is desired that D' be approximately 0.
The relation among the size of beam, wave length and the system's F-Number is as follows: EQU d=k*(F/#)*.lambda. (5)
where d is diameter of beam spot, .lambda. is wave length of incident light, and k is a constant.
For the incident light toward a circular aperture, k is 2.44 and the depth of focus (d') of the scanning light beam is expressed in the following formula: EQU d'=.+-.2*.lambda.*(F/#).sup.2 ( 6)
When it is desired that the diameter of the beam spot (d) be smaller, the wave length .lambda. or F/# should be smaller. This makes the depth of focus (d') shorter because it is in direct proportion to the F/# squared.
It is also desired that both the tangential image surface and sagittal image surface be within the depth of focus (d') when a light beam passes through the lens system. When this is achieved, a high performance output can be obtained in the optical system. Accordingly, it is critical to determine the value of F/# in an optical system.
Because the value of F/# in the constant-speed scanning lens system is usually a somewhat large value, spherical aberration and coma aberration caused by the light beam passing through the lens system are not too important. On the other hand, astigmatism aberration and distortion aberration are key factors.
To conclude, the aberration of distortion on the screen surface 5 should satisfy the demand of the system in order that the D' in formula (4) approaches zero. Additionally, the tangential image surface and the sagittal image surface sagittal plane should be within the depth of focus (d'). The output of such an optical system can approach the diffraction limit.
In order to achieve these desired results, lens systems have been developed as described in the aforesaid U.S. patents. However, these systems were bulky and inconvenient because they required a plurality of lenses and, in addition, did not have an adequately wide scanning angle.